3.7 problem 3

Internal problem ID [5186]

Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 3.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {x^{2} y^{\prime }+2 x y-1=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 11

dsolve(x^2*diff(y(x),x)+2*x*y(x)=1,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {c_{1}+x}{x^{2}} \]

Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 13

DSolve[x^2*y'[x]+2*x*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x+c_1}{x^2} \\ \end{align*}